I am not sure or don't notice the dry mouth. As far as colds no, but I have had one now for over a week. I woke up at 3 am this morning, and my face is swollen and I am in so much pain with that one side. I am going to have to call the dentist today and see if they can take me early.
As far as your shortness of breath question, I don't know, I have been recovering for around 7 weeks since they found all this, so I have not been exercising to speak of.